Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-12T06:49:24.432Z Has data issue: false hasContentIssue false
  • English
  • Français

Pseudo-conservation laws in cyclic-service systems

Published online by Cambridge University Press:  14 July 2016

O. J. Boxma  and
W. P. Groenendijk
O. J. Boxma
Affiliation:
Centre for Mathematics and Computer Science, Amsterdam
W. P. Groenendijk*
Affiliation:
Centre for Mathematics and Computer Science, Amsterdam
*
∗Postal address: Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers single-server, multi-queue systems with cyclic service. Non-zero switch-over times of the server between consecutive queues are assumed. A stochastic decomposition for the amount of work in such systems is obtained. This decomposition allows a short derivation of a ‘pseudo-conservation law' for a weighted sum of the mean waiting times at the various queues. Thus several recently proved conservation laws are generalised and explained.

Keywords

QUEUEING SYSTEMSWITCH-OVER TIMESMEAN WAITING TIMECONSERVATION LAW
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 4 , December 1987 , pp. 949 - 964
Copyright
Copyright © Applied Probability Trust 1987 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Boxma, O. J. (1984) Two symmetric queues with alternating service and switching times. In Performance '84 , ed. Gelenbe, E., North-Holland, Amsterdam, 409–431.Google Scholar
[2] Boxma, O. J. (1986) Models of two queues: a few new views. In Teletraffic Analysis and Computer Performance Evaluation , eds. Boxma, O. J., Cohen, J. W. and Tijms, H. C., North-Holland, Amsterdam, 75–98.Google Scholar
[3] Boxma, O. J. and Meister, B. (1986) Waiting-time approximations for cyclic-service systems with switch-over times. Performance Eval. Rev. 14, 254–262.CrossRefGoogle Scholar
[4] Bux, W. and Truong, H. L. (1983) Mean-delay approximations for cyclic-service queueing systems. Performance Eval. 3, 187–196.CrossRefGoogle Scholar
[5] Cohen, J. W. (1987) A two-queue model with semi-exhaustive alternating service. Performance '87. To appear.Google Scholar
[6] Ferguson, M. J. and Aminetzah, Y. J. (1985) Exact results for nonsymmetric token ring systems. I.E.E.E. Trans. Communications 33, 223–231.CrossRefGoogle Scholar
[7] Fuhrmann, S. W. (1985) Symmetric queues served in cyclic order. Operat. Res. Letters 4, 139–144.Google Scholar
[8] Fuhrmann, S. W. and Cooper, R. B. (1985) Stochastic decompositions in the M/G/1 queue with generalised vacations. Operat. Res. 33, 1117–1129.Google Scholar
[9] Kleinrock, L. (1976) Queueing Systems , Vol. 2. Wiley, New York.Google Scholar
[10] Ott, T. J. (1984) On the M/G/1 queue with additional inputs. J. Appl. Prob. 21, 129–142.CrossRefGoogle Scholar
[11] Schrage, L. (1970) An alternative proof of a conservation law for the queue G/G/1. Operat. Res. 18, 185–187.Google Scholar
[12] Takagi, H. (1984) Mean message waiting time in a symmetric polling system. In Performance '84 , ed. Gelenbe, E., North-Holland, Amsterdam, 293–302.Google Scholar
[13] Takagi, H. (1986) Analysis of Polling Systems. The MIT Press, Cambridge, Mass.Google Scholar
[14] Watson, K. S. (1984) Performance evaluation of cyclic service strategies — a survey. In Performance '84 , ed. Gelenbe, E., North-Holland, Amsterdam, 521–533.Google Scholar
[15] Wolff, R. W. (1982) Poisson arrivals see time averages. Operat. Res. 30, 223–231.CrossRefGoogle Scholar